reserve s for set,
  i,j for Nat,
  c,c1,c2,c3 for Complex,
  F,F1,F2 for complex-valued FinSequence,
  R,R1,R2 for i-element complex-valued FinSequence;

theorem
  Product (c*R) = Product (i|->c) * Product R
proof
  reconsider s=c as Element of COMPLEX by XCMPLX_0:def 2;
  thus Product (c*R) = Product mlt(i|->s,R) by Th27
    .= Product (i|->c) * Product R by Th48;
end;
